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New nonparametric statistics and a criterion (test) based on them are proposed to check the hypothesis of homogeneity of three and two samples, where one sample contains an even number of elements and, hence, can be divided into two samples, against an alternative hypothesis, which implies that random values of one sample are stochastically greater than random values of two other samples. The test is mainly sensitive to shifts of distributions and is more powerful than the Wilcoxon-Mann-Whitney and Whitney tests, at least for problems with samples from exponential and uniform distributions.

An effective algorithm of predicting the trend (deterministic basis) m(t) of a steady (in a wide sense) random process X(t) is proposed. The initial information about the random process X(t) is limited to the assumption that its mean value (mathematical expectation) is equal to zero. The interval [0, T] of observation of the trend sum m(t) and the sample x(t) of the random process X(t) is assumed to be finite. Construction of a prediction estimate μ(T + τ), where τ is the prediction interval, ensures automatic allowance for statistical characteristics of the random process X(t).

Based on an analysis of asymptotic properties of a family of nonparametric decision functions in the pattern recognition problem, a method for synthesizing the structure of this family is proposed.

This paper considers the problem of reducing the computation time in the formation of a single image based on its individual fragments using the sliding window method. A payoff function is obtained. Numerical simulation helped demonstrating the effect of the measurement error and the window size on the accuracy of determination of the shift coordinates of the fragments. The choice of the form of the functional and the window size is substantiated.

Improved algorithms for calculating oil saturation based on the cross-plot method are considered. Oil saturation is determined by comparing analytical parameters obtained by well logging and the corresponding parameters of physical reservoir models that are specifically created at metrological centers. The application of cluster analysis to this problem are discussed. Testing was performed on real data.

This paper considers retrial queueing (RQ) systems with Poisson (elementary) and Markovmodulated Poisson processes. The study is performed by the method of asymptotic cumulants using the theory of vector characteristic functions and the matrix form of equations, which makes it possible to obtain asymptotic results for the whole class of models. The analysis of a single-line RQ system performed revealed the range of applicability of asymptotic results for prelimit situations.

A scanning tunneling microscope equipped with an attachment for high-resolution tunneling spectroscopy is described. The electronic unit of the microscope provides advance of the needle, scanning, and measurement of the tunneling current, and has means for coupling with a tunnel current spectrometer. The spectrometer uses a modulation procedure for measuring the second derivative of the volt-ampere characteristic of the tunneling gap and has a sensitivity of up to 0.25 pA for a modulating signal amplitude of 2 mV.

The current status of ellipsometric methods and hardware tools developed at the Rzhanov Institute of Semiconductor Physics of the Siberian Branch of the Russian Academy of Sciences is considered. A unique static scheme for ellipsometric measurements is presented, which is used as a basis for instruments designed for various purposes: spectral and laser ellipsometers and also ellipsometers for local measurements. The capabilities of ellipsometric instruments are illustrated by results of studying various objects and fast processes. It is demonstrated that complete experiments can be performed with the use of static-type ellipsometers with determination of all parameters of partly depolarized light.

A retrospective analysis of growing of multilayered and variband structures based on the mercury cadmium telluride compounds by the method of molecular beam epitaxy with ellipsometric control and methodical developments in the field of ellipsometry of inhomogeneous structures is presented. Calculations are performed, and solutions of direct and inverse problems for some cases important for practice are obtained. The high accuracy of determining the thickness and composition of the layers in growing heterostructures of nanometer-scale thicknesses is demonstrated. In some cases, it is proposed to use the relative derivative of ellipsometric parameters measured in the course of growing the structure to increase the accuracy of solving the inverse problem. This procedure allows the profiles of the optical constants of structures with gradient compositions to be determined. Theoretical calculations for periodic layered structures are performed, and the possibility of their controlled growing is demonstrated in experiments.

This paper presents a brief review of the progress in the development of two types of semiconductor emitters based on semiconductor Bragg microcavities. The first type of these emitters is a vertical-cavity laser based on Al_xGa_1−xAs. The laser demonstrates stable single-mode lasing ata wavelength of 795 nm, which opens prospects for its use in miniature atomic frequency standards on the basis of Rb⁸⁷. The second type is a single-photon emitter based on semiconductor quantum dots. The design of such an emitter was developed on the basis of a semiconductor Bragg microcavity providing a high level of external quantum efficiency of the emitter (up to 80%) and high performance due to the Purcell effect.